[Kantorovich Duality [1]}]

Let \((X,\mu )\)  and \((Y,\nu )\)  be two Polish probability spaces and let \(c:X\times Y\mapsto \mathbb {R}~\cup \lbrace \infty \rbrace \)  be a semi-continuous cost function, such that
\(\forall (x,y)\in X\times Y, ~~~c(x,y)\ge a(x)+b(y)\) 
